Epitaxial thin films, stress

Consider an elastic material subjected to an equi-biaxial state of stress, characteristic of a uniform epitaxial thin film coherently bonded to a substrate in the presence of lattice mismatch. This is the state of stress that develops in the film when the alloy with spatially uniform compo-... 

Chiu, C.-H. and Gao, H. (1995), A numerical study of stress controlled surface diffusion during epitaxial film growth. Thin films Stresses and mechanical... 

Epitaxial growth of thin films usually involves the formation of strained material as a result of mismatch between the film and substrate and because of the large surface to volume ratio in the film. Surface stress can be a major factor, even when the lattice constants of film and substrate are perfectly matched. Although it appears to be difficult to eliminate the stress totally, it is important to be able to control it and even use it to produce desired qualities. 

Huse has pointed out that strain is to be expected in most thin-film systems, since even in the incommensurate case the intrinsic surface stress will strain the film (18). As a result, we conclude that incomplete wetting is expected for all crystalline films, except in the case where there is an epitaxial relationship between film and substrate and that the film is maintained at its bulk equilibrium lattice spacing. 

Oh S. H. and Jang H. M., Enhanced thermodynamic stability of tetragonal-phase field in epitaxial Pb(Zr,Ti)03 thin films under a two-dimensional compressive stress, Appl. Phys. Lett. 72 (1998) pp.1457-1460. 

One of the most frequently observed phenomena in epitaxial growth is the formation of strain relief patterns. These are caused by the mismatch of the unit cell size of the substrate and the deposited film. In many cases the strain or stress, which is imposed on the thin film by fhe subsfrafe lattice is relieved by reconstruction of the film. This reconsfrucfion can but must not necessarily lead to a nanopatterned film. An inferesfing example is the growth of Ag on Pt(l 11) (see Fig. 10) [41]. It has been shown for this particular system that the first Ag layer grows pseudomorphically exhibiting an isotropic compressive strain of 4.3% whereas in higher layers this strain is relieved by the formation of a dislocation network [42-47]. In order to improve the long-... 

Rossetti Jr., G.A., Cross, L.E., Kushida, K. Stress induced shift of the Curie point in epitaxial PbTiOs thin films. Appl. Phys. Lett. 59, 2524-2526 (1991)... 

Suppose that a thin film is bonded to one surface of a substrate of uniform thickness hs- It will be assumed that the substrate has the shape of a circular disk of radius R, although the principal results of this section are independent of the actual shape of the outer boundary of the substrate. A cylindrical r, 0, z—coordinate system is introduced with its origin at the center of the substrate midplane and with its z—axis perpendicular to the faces of the substrate the midplane is then at z = 0 and the film is bonded to the face at z = hs/2. The substrate is thin so that hs R, and the film is very thin in comparison to the substrate. The film has an incompatible elastic mismatch strain with respect to the substrate this strain might be due to thermal expansion effects, epitaxial mismatch, phase transformation, chemical reaction, moisture absorption or other physical effect. Whatever the origin of the strain, the goal here is to estimate the curvature of the substrate, within the range of elastic response, induced by the stress associated with this incompatible strain. For the time being, the mismatch strain is assumed to be an isotropic extension or compression in the plane of the interface, and the substrate is taken to be an isotropic elastic solid with elastic modulus Es and Poisson ratio Vs the subscript s is used to denote properties of the substrate material. The elastic shear modulus /Xg is related to the elastic modulus and Poisson ratio by /ig = Es/ 1 + t s). 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

A single crystal alloy thin film with composition Sio.ssGeo.is is grown on an initially flat Si(OOl) substrate which is 0.5 mm thick. The lattice parameter of Si at room temperature is asi = 0.5431 nm, while that of Ge is ace = 0.5656 nm. Any dislocations formed as a consequence of epitaxial mismatch between the film and the substrate are known to be 60° dislocations with Burgers vectors in the family represented by (6.18). Assume that the biaxial moduli of Si(OOl) and Ge(OOl) crystals are Mgi(ooi) = 180.5 GPa and MGe(ooi) = 142 GPa, respectively, that the Poisson ratio of the film is i/f R 0.25, that Vq = 6/2, and that 6 w 0.4 nm. Curvature measurements are made continuously using the multibeam optical stress sensor method (see Section 2.3.2) so as to monitor the evolution of internal stress during film deposition. Estimate the substrate curvature at which misfit dislocations are first able to form at the interface between the film and the substrate. 

Koch, R. (1994), the intrinsic stress of polycrystalline and epitaxial thin metal films, Journal of Physics Condensed Matter 6, 9519-9550. 

Vilmin and Raphael [65], predicted that an in-plane pre-stress in elastic polymer films may cause the occurrence of destabilization analogous to the Asaro-Tiller-Grinfeld instability, well-known in the process of thin film growth by molecular beam epitaxy [66, 67]. In a later publication, Closa, Ziebert and Raphael discussed in more detail the conditions for this instability [68]. In particular, they showed that, by having surface difiusion in conjunction with a kinematic boundary condition at the free surface, the Asaro-Tiller-Grinfeld instability can occur. But in the absence of surface diflusion, this instability cannot develop, unless if an un-physically large compression (corresponding to an unreasonable stretch ratio X of >0.03) is applied across the film [68]. 

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